Mathematics and Statistics in the Social Sciences

Over the years, mathematics and statistics have become increasingly important in the social sciences. A look at the history quickly confirms this claim. At the beginning of the 20 century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in the formulation and establishment of them. Moreover, many practitioners considered mathematical methods to be inappropriate and simply not suited to foster our understanding of the social domain. Notably, the famous Methodenstreit was also about the role of mathematics in the social sciences. Here mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical and especially statistical methods were standardly used and it became relatively uncontested that they are of much value in the social sciences. In fact, the use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and to form hypotheses, and almost all of them use (to a greater or lesser extend) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new sub-disciplines, and the establishment of specialized journals and societies. And indeed, sub-disciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies, such such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments happened in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a